Reducing Peak to Average Power Ratio of OFDM by Using Selected Mapping

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(1)IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. International Journal of Research in Information Technology (IJRIT) www.ijrit.com. ISSN 2001-5569. Reducing Peak to Average Power Ratio of OFDM by Using Selected Mapping Vineet Kumar Singh1, Er. Anuj Goel2, Er. Abhishek Sharma3 1. M.Tech Final Year Student, Deptt. Of ECE, MMEC, MMU, Mullana Ambala, Haryana, India [email protected] 2. Assistant Professor, Deptt of ECE, MMEC, MMU, Mullana Ambala, Haryana, India [email protected]. 3. Assistant Professor, Deptt of ECE, MMEC, MMU, Mullana Ambala, Haryana, India [email protected]. ABSTRACT Orthogonal Frequency Division Multiplexing (OFDM) is considered to be a promising technique against the multipath fading channel for wireless communications. However, OFDM faces the Peak-to-Average Power Ratio (PAPR) problem that is a major drawback of multicarrier transmission system which leads to power inefficiency in RF section of the transmitter. This paper present different PAPR reduction techniques and conclude an overall comparison of these techniques. We also simulate the selected mapping technique (SLM) for different route number which is most efficient technique for PAPR reduction when the number of subcarrier is large. Simulation shows that the PAPR problem reduced as the route number increases. Keywords: Orthogonal Frequency Division Multiplexing (OFDM), Peak-to-Average Power Ratio (PAPR), Power Amplifiers (PAs), Selected Mapping (SLM), Complementary Cumulative Distribution Function (CCDF).. 1. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) technology is one of the most attractive candidates for fourth generation (4G) wireless communication. It effectively combats the multipath fading channel and improves the bandwidth efficiency. At the same time, it also increases system capacity so as to provide a reliable transmission [1]. OFDM uses the principles of Frequency Division Multiplexing (FDM) [2] but in much more controlled manner, allowing an improved spectral efficiency [1]. The basic principle of OFDM is to split a high-rate data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers. These subcarriers are overlapped with each other. Because the symbol duration increases for lower rate parallel subcarriers, the relative amount of dispersion in time caused by multipath delay spread is decreased. Inter-symbol interference (ISI) is eliminated almost completely by introducing a guard time in every OFDM symbol. OFDM faces several challenges. Therefore, reducing the PAPR is of practical interest. Many PAPR reduction methods have been proposed. Some methods are designed based on employing redundancy, such as coding [4], [5], selective mapping with explicit or implicit side information [6], [3], or tone reservation [10]. An apparent effect of using redundancy for PAPR reduction is the reduced transmission rate. PAPR reduction may also be achieved by using extended signal constellation, such as tone Vineet Kumar Singh, IJRIT. 400.

(2) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. injection [10], or multi-amplitude CPM. The associated drawback is the increased power and implementation complexity. A simple PAPR reduction method can be achieved by clipping the time-domain OFDM signal. In this work, we survey the PAPR reduction techniques for OFDM. We also present PAPR reduction technique based on selective mapping (SLM) under different route number M. The remainder of this paper is organized as follows. In section 2, some basics definition about PAPR in OFDM is given. Section 3, describes PAPR reduction techniques. In Section 4 the overall analysis of different techniques is given. Section 5 describes the simulation results. Conclusions are given in section 6.. 2. PAPR Definition Theoretically, large peaks in OFDM system can be expressed as Peak-to-Average Power Ratio, or referred to as PAPR. The PAPR, for a continuous time signal x(t) is defined as: (1) |

(3) | = 0 ≤ ≤ |

(4) | . The PAPR for discrete time signals can be estimated by oversampling the vector d by a factor L and computing NL-point IFFT. The PAPR in this case is defined as: =. |

(5) | = 0,1, … , − 1 |

(6) | . (2). PAPR, in quantitative terms, is usually expressed in terms of Complementary Cumulative Distribution function (CCDF) for an OFDM signal, and is mathematically given by >

(7) = 1 − 1 − .

(8). !" #. (3). Where, PAPR0 is the clipping level. This equation can also be read as the probability that the PAPR of a symbol block exceeding some clip level PAPR0.. 3. PAPR REDUCTION TECHNIQUES Several PAPR reduction techniques have been proposed in the literature. These techniques are divided into two groups. These are signal scrambling techniques and signal distortion techniques.. 3.1 Signal Scrambling Techniques: Block Coding Techniques, Selected mapping (SLM), Partial Transmit Sequence (PTS), Interleaving Technique, Tone Reservation (TR) and Tone Injection (TI) etc are Signal Scrambling Techniques.. 3.1.1 Block coding Technique The coding technique [4] is used to select such codeword’s that minimize or reduce the PAPR. It causes no distortion and creates no out-of-band radiation, but it suffers from bandwidth efficiency as the code rate is reduced. It also suffers from complexity to find the best codes and to store large lookup tables for encoding and decoding, especially for a large number of sub carriers.. 3.1.2 SLM for reducing PAPR The block diagram of SLM technique for reducing PAPR is shown in Figure 1. In this approach, it is assumed that M OFDM symbols carry the same information and that these are statistically independent of each other. In this case, the probability of PAPR greater than z is equal to the product of each independent signal and can be written as $%& > '

(9) = $%& > '

(10)

(11) ( =. 1 − exp −'

(12)

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(14) (. Vineet Kumar Singh, IJRIT. (4). 401.

(15) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. In SLM method, shown in Figure 1, firstly M statistically independent sequences which represent the same information are generated, and next, the resulting M statistically independent data blocks ,- = /,-, , ,-,0 , … , ,-,#0 1 2 , m=1,2,…,M are then forwarded into IFFT operation simultaneously. Finally, at the receiving end, OFDM symbols - = /0 , , … , # 1 2 in discrete time-domain are acquired, and then the PAPR of these M vectors are calculated separately. The sequences 3 with the smallest PAPR will be elected for final serial transmission. The SLM method has been proven to significantly improve the PAPR performance of OFDM system.. Figure 1: Basic principle of SLM technique for reducing PAPR.[2]. It is because the data blocks ,- = /,-, , ,-,0 , … , ,-,#0 1 2 , m=1, 2… M is statistical independent. Assuming, that for a single OFDM symbol, the CCDF probability of PAPR larger than a threshold is equals to p. Then, the general probability of PAPR larger than a threshold for k OFDM symbols can be expressed as pk. This illustrates that the new probability obtained by SLM algorithm is much smaller compared to the original. The key point of selected mapping method lies in how to generate multiple OFDM signals when the information is same. For this purpose, firstly different pseudo-random sequences - = /-, , -,0 , … , -,#0 1 2 , m=1,2,…,M, are defined; where -,4 = 567,8 and stands for the rotation factor. -,4 is also known as the weighting factor and 9-,4 is uniformly distributed in [0 2π]. The N different sub-carriers are modulated with these vectors respectively so as to generate candidate OFDM signals. This process can also be seen as performing dot product operation on a data block :4 with rotation factor - . In practise, all the elements of phase sequence 0 are set to 1 so as to make this branch sequence the original signal. The symbols in branch m can be expressed as ,- = /: -,, :0 -,0,…., :#0 -,#0 12 , = 1,2, … , =. (5). These M OFDM frames are then transformed from frequency domain to time domain by performing IFFT calculation. The entire process can be mathematically expressed as -

(16) =. 0. √#. ∑#0 :4 -,4 . 5 @4∆BC , 0 ≤ D ≤ , = 1,2, … , = . (6). Finally, the one which possess the smallest PAPR value is selected for transmission. Its mathematical expression is given as 3 = EFG0H-H( -

(17). (7). Where, argmin(.) represent the argument with minimum value. At the receiver, in order to correctly demodulate the received signal, it is necessary to know which sequence is linked to the smallest PAPR among M different candidates after performing the dot product. Thus, the receiver is required to learn information about selected phase vector sequence and ensure that the vector sequence is received correctly. An intuitive approach is to select the whole sequence of branch number m as side information transmitted to Vineet Kumar Singh, IJRIT. 402.

(18) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. the receiving end. However in practice, the process does not necessarily require the delivery of the entire vector sequence. It can be realized by sending the route number of the vector sequence instead. This is only possible when the receiving end is able to restore the random phase sequence by means of look-up table or any other method. As the side information plays a vital role for signal restoration at the receiver, channel coding is used to guarantee a reliable transmission. Once channel coding technique is adopted during the data transmission process, sending of any additional side information is not required. In this way, all possible routes are detected at the receiving end from which the most likely one is chosen as the optimum. 3.1.3 Partial Transmit Sequence: In the PTS technique, input data block X is partitioned into M disjoint sub–blocks Xm = [Xm,0, Xm,1,…..,Xm,N= 1,2,….,M and the sub-blocks are combined to minimize the PAPR in time domain. The L times oversampled time domain signal of Xm, m = 1,2,..M, is obtained by taking the IDFT of length NL on Xm concatenated with (L-1)N zeros. These are called the partial transmit sequences. Complex phase factors are introduced to combine the PTS sequences. The set of phase factors is denoted as a vector b = [b1, b2, …,bm]T. The time domain signal after combining is given by T 1] , m. -. J = K I- . I

(19). (8). -L0. Where x'(b) = [x'0(b), x'1(b)…x'NL-1(b)]T. The objective is to find the set of phase factors that minimizes the PAPR. 3.1.4 Tone Reservation (TR) The main idea of this method is to keep a small set of tones for PAPR reduction. This can be originated as a convex problem and this problem can be solved accurately. Tone reservation method is based on adding a data block and time domain signal. A data block is dependent time domain signal to the original multicarrier signal to minimize the high peak. This time domain signal can be calculated simply at the transmitter of system and stripped off at the receiver. The amount of PAPR reduction depends on some factors such as number of reserved tones, location of the reserved tones, amount of complexity and allowed power on reserved tones This method explains an additive scheme for minimizing PAPR in the multicarrier communication system[24]. It shows that reserving a small fraction of tones leads to large minimization in PAPR ever using with simple algorithm at the transmitter of the system without any additional complexity at the receiver end. Here, N is the small number of tones, reserving tones for PAPR reduction may present a non–negligible fraction of the available bandwidth and resulting in a reduction in data rate. The advantage of TR method is that it is less complex, no side information and also no additional operation is required at the receiver of the system.. 3.1.5 Tone Injection Technique (TI) This technique is based on general additive method for PAPR reduction. Using an additive method achieves PAPR reduction of multicarrier signal without any data rate loss. TI uses a set of equivalent constellation points for an original constellation points to reduce PAPR. The main idea behind this method is to increase the constellation size. Then, each point in the original basic constellation can be mapped into several equivalent points in the extended constellation, since all information elements can be mapped into several equivalent constellation points. These additional amounts of freedom can be utilized for PAPR reduction. The drawbacks of this method are; need to side information for decoding signal at the receiver side, and cause extra IFFT operation which is more complex.. 3.2 Signal Distortion Techniques 3.2.1 Peak Windowing. Vineet Kumar Singh, IJRIT. 403.

(20) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. The peak windowing method has been suggested by Van Nee and Wild. This method, proposes that it is possible to remove large peaks at the cost of a slight amount of self interference when large peaks arise infrequently. Peak windowing reduces PAPRs at the cost of increasing the BER and out-of-band radiation. Clipping is a one kind of simple introduces PAPR reduction technique which is self interference. The technique of peak windowing offers better PAPR reduction with better spectral properties. In peak windowing method we multiply large signal peak with a specific window, for example; Gaussian shaped window, cosine, Kaiser and Hamming window. In view of the fact that the OFDM signal is multiplied with several of these windows, consequential spectrum is a convolution of the original OFDM spectrum with the spectrum of the applied window. Thus, the window should be as narrow band as possible, conversely the window should not be too long in the time domain because various signal samples are affected, which results an increase in bit error rate (BER). Windowing method, PAPRs can be obtained to 4dB which from the number of independent subcarriers. The loss in signal-to-noise ratio (SNR) due to the signal distortion is limited to about 0.3dB. A back off relative to maximum output power of about 5.5dB is needed in spectra distortion at least 30dB below the in-band spectral density.. 3.2.2 Envelope Scaling The Envelope Scaling technique has been proposed by Foomooljareon and Fernando. They anticipated a new algorithm to reduce PAPR by scaling the input envelope for some subcarriers before they are sent to IFFT. They used 256 subcarriers with QPSK modulation technique, so that envelopes of all the subcarriers are equal. The key idea of this scheme is that the input envelope in some sub carrier is scaled to achieve the smallest amount of PAPR at the output of the IFFT. Thus, the receiver of the system doesn’t need any side information for decoding the receiver sequence. This scheme is appropriate for QPSK modulation; the envelopes of all subcarriers are equal. Results show that PAPR can be reduced significantly at around 4 Db.. 3.2.3. Clipping and Filtering:. This is the simplest technique used for PAPR reduction. Clipping means the amplitude clipping which limits the peak envelope of the input signal to a predetermined value.Let x[n] denotes the pass band signal and xc[n] denotes the clipped version of x[n],which can be expressed as − /1 ≤ − M /1 = N /1|/1| < /1 ≥ . (9). Where, A is the pre-defined clipping level. However this technique has several drawbacks, such as clipping causes in-band signal distortion, resulting in Bit Error Rate performance degradation. It also causes out-ofband radiation, which imposes out-of-band interference signals to adjacent channels. This out-of-band radiation can be reduced by filtering. This filtering of the clipped signal further leads to the peak re-growth; which means the signal after filtering operation may exceed the clipping level specified for the clipping operation.. 4. Overall Analyses of Different Techniques There are several techniques has been proposed in literature. Thus, it is possible to reduce the large PAPR by using the different techniques. Note that the PAPR reduction technique should be chosen with awareness according to various system requirements. There are many issues to be considered before using the PAPR reduction techniques in a digital communication system. These issues include PAPR reduction capacity, power increase in transmit signal, BER increase at the receiver, loss in data rate, computational complexity increase and so on. Simultaneously most of the techniques are not proficient to obtain a large reduction in PAPR with low coding overhead, with low complexity, without performance degradation and without transmitter and receiver symbol handshake. Table1, summarizes advantages and drawbacks of various techniques presented to reduce PAPR in OFDM systems. Table1. Comparison of PAPR Reduction Techniques. Vineet Kumar Singh, IJRIT. 404.

(21) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. Techniques Clipping and Filtering. Distortion Yes. Power Increase No. Data Rate Loss No. Coding Partial Transmit Sequence Tone Reservation Tone Injection ACE Selected Mapping. No No No No No No. No No Yes Yes Yes No. Yes Yes Yes No No Yes. 5. SIMULATION OF SLM SCHEME Case I: Comparison of PAPR reduction performance with different values of M while number of subcarriers (N) is fixed at 128. It seems that that the ability of PAPR reduction using SLM is affected by the route number M and subcarrier number N. Therefore, simulation with different values of M and N and the results exhibits some desired properties of signals representing same information. Comparison of PAPR reduction performance with different values of M while N is fixed at 128. Rotation factor is defined as-,4 ∈ /R1, RS1. From Figure2; it can be observed that the SLM method displays a significant level of PAPR reduction compared to the original OFDM signal. It can also be noted that increasing M leads to the improvement of PAPR reduction performance. In order to evaluate performance, the probability is set to 1% and then the CCDF curves with different M values are compared. The PAPR value in case of M=2 is about 1dB smaller than the unmodified one M=1. Under the same condition, the PAPR value of case M=16 is about 3dB smaller than the original one M=1. However, from the comparison of the curve M=8 and M=16, it can be observed that the performance difference between these two cases is less than 0.5dB. This proves that it is difficult to achieve a linear growth of PAPR reduction performance with further increase in the value of M (like M>=8). Therefore in practical applications, it is preferred to take M=8, so as to avoid introducing too much computational complexity.. Figure 2: Performance of SLM PAPR reduction scheme with different values of M.. Vineet Kumar Singh, IJRIT. 405.

(22) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. Case II: Comparison of PAPR reduction performance with different number of subcarriers (N) values; while, M is fixed at 8. It can be seen from Figure 3. that SLM algorithm is particularly suitable for OFDM with large number of sub-carriers. Thus from the above made discussion, SLM approach can significantly reduce the PAPR of OFDM signals. The increase of the number of OFDM signal frames M will raise the complexity dramatically; but, with benefit of small improvement of PAPR reduction performance. SLM algorithm can be adapted to any length of FFT frame; which means it can be used for different OFDM systems with different number of carriers. It is particularly suitable for the OFDM system with a large number of subcarriers (more than 128). In terms of complexity, every time when SLM algorithm is applied, it requires calculating the M group IFFTs at the transmitter compared to only one on ordinary OFDM system, and its M # points IFFT operation needs complex multiplication and T33 = =. UVF addition, separately. These. problems usually pose high difficulties on real OFDM implementation; therefore, it is required to reduce the computational complexity. Therefore in practical applications, to compromise with the computing complexity and improve the performance, M<=8 is usually taken. .. Figure 1.2: Performance of SLM PAPR reduction technique for different values of N. 6.. CONCLUSION. We describe and summarize several techniques of PAPR and simulate SLM technique which is the best solution for PAPR. The selected technique provides us with a good range in performance to reduce PAPR problem. SLM algorithm adapted to any length of route number that means it can be used for different OFDM systems with different number of carriers. It is particularly suitable for the OFDM system with a large number of sub-carriers (more than 128). This research will continue in directions Firstly, PAPR reduction concepts will be expanded for distortion less transmission and identifying the best alternatives in terms of performance increase Secondly, PAPR reduction technique will be develop for low data rate loss and efficient use of channel. A study of the complexity issues of the PAPR reduction technique is required, especially looking at ways of further.. Vineet Kumar Singh, IJRIT. 406.

(23) IJRIT International Journal of Research in Information Technology, Volume 2, Issue 4, April 2014, Pg: 400- 407. REFERENCES [1] H. Li, T. Jiang and Y. Zhou (2011), “An Improved Tone Reservation Scheme With Fast Convergence for PAPR Reduction in OFDM Systems”, IEEE Transactions on Broadcasting, Vol. 57, No. 4, pp. 902-06. [2] H. B. Jeon, J. S. and D. J. Shin (2011), “A Low-Complexity SLM Scheme Using Additive Mapping Sequences for PAPR Reduction of OFDM Signals”, IEEE Transactions on Broadcasting, Vol. 57, No. 4, pp.866-75. [3] Md. Abdullah Al Baki, Mohammad Zavid Parvez “PEAK TO AVERAGE POWER RATIO (PAPR) REDUCTION IN OFDM BASED RADIO SYSTEMS” Electrical Engineering Blekinge Institute of Technology, May 2010. [4] K. Kasiri and M. J. Dehghani (2009), “A Blind SLM Scheme for Reduction of PAPR in OFDM Systems”, World Academy of Science, Engineering and Technology, pp. 399-402. [5] Krongold, B. S. and D. L. Jones, “PAR reduction in OFDM via active constellation extension,” IEEE Trans. on Broadcasting, Vol. 49, 258–268, Sept. 2003.. [6] Oh-Ju Kwon and Young-Ho Ha, “Multi-carrier PAPR reduction method using sub-optimal PTS with threshold,” IEEE Transactions on Broadcasting, June. 2003, vol. 49, no. 2, PP. 232-53 [7] Davis, J. A. and J. Jedwab, “Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes,” IEEE Trans. Inform. Theory, Vol. 45, 2397–2417, Nov. 1999. [8] Xiaodong Li and Leonard J. Cimini, "Effects of Clipping and Filtering on the Performance of OFDM ," IEEE Communications Letters , Vol. 2, No. 5, May 1998. [9] Wilkison, T. A. and Jones A. E., "Minimization of the Peak to mean Envelope Power Ratio of Multicarrier Transmission Schemes by Block Coding," IEEE, Vehicular Conference, Vol.2, Jul. 1995 [10] Gross, R. and D. Veeneman, “Clipping distortion, in DMT ADSL systems,” IEEE Electron. Lett., Vol. 29, 2080–2081, Nov. 1993.. Vineet Kumar Singh, IJRIT. 407.

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